How big (or small) is a nanometer?

To answer this question, and bring the size of a nanometer into perspective, I thought of a simple experiment. The apparent image size (s) of an object decreases inversely to the distance from it (x). So, I viewed a 3 inch × 3 inch Post-It® note at various distances with a ruler held one arm's length away from my eye. Now how far must I be from the Post-It® note for it to appear, say, 3 nm in size which is about 10 atoms placed next to each other?

Here are the results of my experiment:

Amazingly, the graph of image size versus distance agrees fairly well with the expected (inverse) relation.

I take the constant of 2.50 Paces-inch as the true value (for my eye). Assuming each of my paces is one meter and converting inches to centimeters the constant becomes, 6.35 cm-m.

Now it is possible to calculate the size of the Post-It® note a given distance away. Assume the note is at a distance equal to traveling half-way around the Earth. The equatorial radius of the Earth is 6.38 × 10⁶ m so one can find the linear distance is:

x = p 6.38 × 10⁶ m = 2.00 × 10⁷ m

Since,

s × x = 6.35 cm-m

it will appear to be:

s = [6.35 cm-m / 2.00 × 10⁷ m] × [10⁷ nm / cm] = 3.17 nm (~ 3 nm).

Interestingly, one must move a Post-It® note a distance equivalent to half-way around the Earth for it to appear 3 nm in size. A nanometer is pretty small...